It is a simple process to claim your free games on Stadia. If you have your Stadia App installed or viewing this the web if you click this link it will bring you to the store. If you need to download the Stadia App you can for Apple devices here and Android here. You will be able to see the selection of games available on Pro to claim. All you need to do then is go into each game and hit claim.
I recommend that you claim each game. As Stadia is a cloud gaming platform you don’t need to download the game and also everything you purchase or claim is always there. There are no storage limits and all your games will be available to play anytime you want them.